Copy the page URI to the clipboard
Rust, Dan and Spindeler, Timo
(2018).
DOI: https://doi.org/10.1016/j.indag.2018.05.013
Abstract
Random substitutions are a natural generalisation of their classical `deterministic' counterpart, whereby at every step of iterating the substitution, instead of replacing a letter with a predetermined word, every letter is independently replaced by a word from a finite set of possible words according to a probability distribution. We discuss the subshifts associated with such substitutions and explore the dynamical and ergodic properties of these systems in order to establish the groundwork for their systematic study. Among other results, we show under reasonable conditions that such systems are topologically transitive, have either empty or dense sets of periodic points, have dense sets of linearly repetitive elements, are rarely strictly ergodic, and have positive topological entropy.
Viewing alternatives
Download history
Metrics
Public Attention
Altmetrics from AltmetricNumber of Citations
Citations from DimensionsItem Actions
Export
About
- Item ORO ID
- 70946
- Item Type
- Journal Item
- ISSN
- 0019-3577
- Project Funding Details
-
Funded Project Name Project ID Funding Body Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications CRC 1283 Bielefeld University - Keywords
- Primitive substitutions; random substitutions; symbolic dynamics
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2018 Royal Dutch Mathematical Society
- Depositing User
- Dan Rust